Question

Consider the following decay series:
$A⟶B⟶C⟶D$
Where, $A$, $B$ and $C$ are radioactive elements with half lives of $4.5$ $sec$, $15$ days and $1$ $sec$ respectively and $D$ is non-radioactive element. Starting with $1$ mole of $A$, the number of moles of $A$, $B$, $C$ and $D$ left after $30$ days are:

• A. One mole of $D$ and none of $A$, $B$ or $C$
• B. $3/4$ mol of $B$, $1/4$ mol of $D$ and none of $A$ or $C$
• C. $1/4$ mol of $B$, $3/4$ mol of $D$ and none of $A$ or $C$
• D. $1/2$ mol of $B$, $1/4$ mol of $C$, $1/4$ mol of $D$ and none of $A$
• E. $1/4$ mol of each $A$, $B$, $C$ and $D$

Answer 1

Answer: (D)

$1/2$ mol of $B$, $1/4$ mol of $C$, $1/4$ mol of $D$ and none of $A$

$\alpha$-decay

${}_Z^{A}X\underrightarrow{-\alpha }{}_{Z-2}^{A-4}Y$

$\beta$-decay

${}_Z^{A}X\underrightarrow{-\beta }{}_{Z+1}^{A}Y$

Now,

${}_Z^{A}X\underrightarrow{-\beta }{}_{Z+1}^{A}Y\underrightarrow{-\alpha }{}_{Z-1}^{A-4}Z$

$\Rightarrow$Atomic number of X is greater than that of Z.

$\Rightarrow$Atomic number of Y is greater than that of Z.

$\Rightarrow$Mass number of X is same as that of Y.

$\therefore$only 3 is correct.